What is a Self-Absorbed Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.

If a word conforms to a special rule, I call it an Self-Absorbed Word™.

Use the following examples below to find the rule.

And, if you want to analyze, here is a CSV version:

Self-Absorbed Words™,Not Self-Absorbed Words™
CAVE,DEN
GNU,EMU
JACK,JOHN
LAME,HURT
MINT,LEAF
PINE,OAK
WINE,GLASS
Less Common Examples:,
BIRD,BEAR
CURL,BEND
FIJI,EVEREST
LIVES,SOULS
PIPER,FLUTIST
HEART,LUNG
PIP,NOTCH

• Haven't you heard of the new big Google project Glass Looks At Someone Smiling? (just kidding). Then there's John Only Has Nine, and Emu Mimics Unix! – ErikE Aug 29 '16 at 17:46
• Why the "™" in Self-Absorbed Word™ ? – Dan Walmsley Aug 29 '16 at 23:53
• @DanWalmsley Because JLee did it and I'm just following in the format they created. – Engineer Toast Aug 30 '16 at 0:05
• @JLee Do you remember why you trademarked the words / phrases? Was it just a hook? – Engineer Toast Aug 30 '16 at 0:05

I'm pretty sure these are

Recursive Acronyms

I recognize

Cave Automatic Virtual Environment, Gnu's Not Unix, Curl URL Request Library, and Wine Is Not an Emulator

Although I'm honestly a little surprised that DEN isn't self-absorbed. I thought I heard of something along those lines once.

Yes, all the self-absorbed words

• /is using GIMP while reading this – Mithical Aug 29 '16 at 14:57
• Would it have been more of a challenge had I left out the "Lesson Common Examples" header and just mixed them all up? I was worried it would be too esoteric a puzzle without it but I may have pushed it too far the other way. – Engineer Toast Aug 29 '16 at 17:03
• @EngineerToast I don't think that would have made much of a difference? The biggest hint for me was the presence of GNU, which is (to me) by far the most unusual word on the list. – Sconibulus Aug 29 '16 at 17:10
• @EngineerToast Yep, as soon as I saw "GNU" I didn't really even need to look at the rest of the list. Take out that word and it would be much more challenging. – Bradley Uffner Aug 29 '16 at 19:06
• @Sconibulus To think, here I left it in specifically to make sure it wasn't too challenging. Ah, well. There'll be a new one tomorrow. – Engineer Toast Aug 29 '16 at 20:01